Question

an airline would like information on which seat is preferred by customers. the airline assumes the majority of customers prefer the window seat, and is looking for evidence to support that claim. the results of a simple random sample of customer seat preference is shown below.

airline customer sample
window seat 196
observations 350
confidence level 0.95
critical value 1.64
test statistic (z) 2.24
p - value 0.0124

identify the population parameter.
pick

what condition for using a z - distribution is met?
pick

what is the level of significance? ex: 0.12

what is the null hypothesis $h_0$? pick

what is the alternative hypothesis $h_a$? pick

should $h_0$ be rejected or does $h_0$ fail to be rejected? pick

what conclusion can be drawn from the data?
pick

Explanation:

Step1: Identify population parameter

The parameter is the proportion of all airline customers who prefer window seats, denoted as \(p\).

Step2: Check z-distribution condition

Calculate sample proportion: \(\hat{p} = \frac{196}{350} = 0.56\)
Verify: \(n\hat{p} = 350*0.56 = 196 \geq 10\), \(n(1-\hat{p}) = 350*(1-0.56) = 154 \geq 10\). Large sample condition is met.

Step3: Find significance level

Significance level \(\alpha = 1 - 0.95 = 0.05\)

Step4: State null hypothesis

\(H_0: p = 0.5\) (no majority preference)

Step5: State alternative hypothesis

\(H_a: p > 0.5\) (majority prefer window seats)

Step6: Make decision

Compare p-value to \(\alpha\): \(0.0124 < 0.05\), so reject \(H_0\).

Step7: Draw conclusion

Rejecting \(H_0\) provides evidence for the airline's claim of majority window seat preference.

Answer:

1. Population parameter: The proportion of all airline customers who prefer window seats
2. Met z-distribution condition: \(n\hat{p} \geq 10\) and \(n(1-\hat{p}) \geq 10\) (or "Sample size is large enough")
3. Level of significance: \(0.05\)
4. Null hypothesis \(H_0\): \(p = 0.5\)
5. Alternative hypothesis \(H_a\): \(p > 0.5\)
6. Decision: Reject \(H_0\)
7. Conclusion: There is sufficient evidence to support the claim that the majority of customers prefer window seats.